There are various kinds of optical elements that have a function of focusing light. Some of those optical elements use refraction, others use diffraction, and still others may use both of these two functions in combination. In this description, an optical element as a combination of an optical element that uses refraction and an optical element that uses diffraction will be referred to herein as a “diffractive lens”. A diffractive lens is obtained by forming a diffraction grating on the refracting surface of a lens and contributes to increasing the number of design parameters for adjusting optical properties. Consequently, with a diffractive lens, the number of lenses required can be reduced with the same optical performance maintained.
It is also well known that a diffractive lens contributes effectively to reducing various kinds of aberrations of a lens including field curvature and chromatic aberration (which is a shift of a focal point with the wavelength). This is partly because a diffraction grating has the opposite type of dispersion property to the one caused by an optical material. Such a dispersion property is sometimes called a “reverse dispersion property”.
The shape of a diffractive lens is a combination of the base shape of a lens body, on which a diffraction grating is to be formed (i.e., the shape of a refractive lens), and the shape of the diffraction grating. For example, FIG. 13(a) illustrates an aspheric shape Sb of a lens body and FIG. 13(b) illustrates a diffraction grating shape Sp1, which is determined by the phase function represented by the following Equations (1):
                                          ϕ            ⁡                          (              r              )                                =                                                    2                ⁢                π                                            λ                0                                      ⁢                          {                                                ψ                  ⁡                                      (                    r                    )                                                  -                                                      λ                    0                                    ⁢                                      int                    ⁡                                          (                                                                        ψ                          ⁡                                                      (                            r                            )                                                                                                    λ                          0                                                                    )                                                                                  }                                      ⁢                                  ⁢                              ψ            ⁡                          (              r              )                                =                                                    a                1                            ⁢              r                        +                                          a                2                            ⁢                              r                2                                      +                                          a                3                            ⁢                              r                3                                      +                                          a                4                            ⁢                              r                4                                      +                                          a                5                            ⁢                              r                5                                      +                                          a                6                            ⁢                              r                6                                      +            …            +                                          a                i                            ⁢                                                r                  i                                ⁢                                                                  (                                                      r                    2                                    =                                                            x                      2                                        +                                          y                      2                                                                      )                                                                        (        1        )            where φ(r) is a phase function represented by the curve Sp in FIG. 13(b), Ψ(r) is an optical path length difference function (z=Ψ(r)), int is an integer operator, r is a radial distance from the optical axis, λ0 is a designed wavelength, and a1, a2, a3, a4, a5, a6, . . . and ai are phase coefficients. As can be seen from FIG. 13(b), in the shape Sp1, a phase step is produced every time the phase goes over 2π.
According to a conventional method for designing the shape of a diffractive lens, supposing there is a diffraction grating on an aspheric shape Sb, an aspheric coefficient that determines an aspheric shape Sb and a phase function that determines a phase function sp are obtained at the same time so that the optical property to be achieved by giving an optical path length difference based on the phase function Sp to the aspheric shape Sb has a desired level. The shape Sbp1 of the diffraction grating surface is determined by adding the shape Sp1 corresponding to the phase difference function to the aspheric shape Sb (see FIG. 13(c)). The height d of the phase step shown in FIG. 13(c) generally satisfies the following Equation (2):
                    d        =                              q            ·            λ                                                              n                1                            ⁡                              (                λ                )                                      -            1                                              (        2        )            where q is a designed order (e.g., q=1 as for first-order diffracted light), λ is the operating wavelength, d is the step height of the diffraction grating, and n1(λ) is the refractive index of a lens material that makes the lens body at the operating wavelength λ. The refractive index of a lens material has a wavelength dependence and is a function of the wavelength. In a diffraction grating that satisfies this Equation (2), the phase difference between the root and the end of a phase step becomes 2π on the phase function, and the optical path difference with respect to light with the operating wavelength λ becomes an integral number of times as long as the wavelength. Consequently, the diffraction efficiency of qth-order diffracted light (which will be referred to herein as “qth-order diffraction efficiency”) with respect to light with the operating wavelength can be approximately equal to 100%.
It is known that in such a diffractive lens, as the error from the relation represented by Equation (2) widens, diffracted light rays of non-designed orders are produced one after another, thus causing flares or ghosts that covers the image field and deteriorating the image quality.
Thus, in order to eliminate such flares to be caused by diffracted light rays of non-designed orders from an image processor that uses such a diffractive lens, Patent Document No. 1 discloses a method for reducing the influence of the flares by detecting the locations of pixels with saturated luminance, estimating the locations and intensities of the flares with respect to those pixel locations, and performing signal processing on the image based on those data.
On the other hand, Patent Document No. 2 discloses a method for reducing the influence of flares on a digital camera that uses a diffractive lens. According to the method of Patent Document No. 2, if there are any saturated pixels when the first frame is shot, the second frame is shot so as to prevent those pixels from getting saturated again and then the image shots of the first and second frames are subjected to computational processing to eliminate flares.